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Chemical Equilibrium Dr. Ron Rusay © Copyright 2003-2010 R.J. Rusay Chemical Equilibrium The reactions considered until now have had reactants react completely to form products. These reactions “went” only in one direction. Some reactions can react in either direction. They are “reversible”. When this occurs some amount of reactant(s) will always remain in the final reaction mixture. Chemical Equilibrium (Definitions) A chemical system where the concentrations of reactants and products remain constant over time. On the molecular level, the system is dynamic: The rate of change is the same in either the forward or reverse directions. Dynamic Equilibrium “The Pennies” • Organize into groups of 4. • Dr. R will provide your group with a number and an accounting form. • In your group, select one person as: 1) Money Keeper 2) Recorder 3) Transfer Agent 4) Auditor •Have the Recorder put everyone’s name on the accounting form. • After recording all of the names send the Money Keeper to see Dr. R. for your capital stake. • Await instructions for phase I. Dynamic Equilibrium “The Pennies” There will be 8 phases. Find your Equilibrium partners eg. IA with IB, IIA with IIB, etc. Phase I: Phase II: G roup Rate initial change final initial change final 1X -30% 40 -12 28 -30% 28 1Y -10% 0 +12 12 -10% 12 2X -30% 20 -6+10 24 -25% 24 2Y -50% 20 -10+6 16 -50% 16 Dynamic Equilibrium “The Pennies” There will be 8 phases. Find your Equilibrium partners eg. IA with IB, IIA with IIB, etc. Phase I: Phase II: G roup Rate initial change final initial change final 1X -30% 40 -12 28 -30% 28 1Y -10% 0 +12 12 -10% 12 2X -30% 20 -6+10 24 -25% 24 2Y -50% 20 -10+6 16 -50% 16 Dynamic Equilibrium “The Pennies” There will be 8 phases. Find your Equilibrium partners eg. IA with IB, IIA with IIB, etc. Phase I: Phase II: G roup Rate initial change final initial change final 1X -30% 40 -12 28 -30% 28 1Y -10% 0 +12 12 -10% 12 2X -30% 20 -6+10 24 -25% 24 2Y -50% 20 -10+6 16 -50% 16 Dynamic Equilibrium “The Pennies” There will be 8 phases. Here are examples of 2 phases with two Equilibrium partners X and Y and two separate groups: 1 and 2. Find your Equilibrium partners eg. IA with IB, IIA with IIB, etc. Phase I: Phase II: G roup Rate initial change final initial change final 1X -30% 40 -12 28 -30% 28 1Y -10% 0 +12 12 -10% 12 2X -30% 20 -6+10 24 -25% 24 2Y -50% 20 -10+6 16 -50% 16 Calculate the change and final amounts for your Phase I, which is the initial amount for Phase II.. Once you are ready, you can begin and go through Phases 1-4 at your own pace. Stop after Phase 4 and await further instructions.. Pennies Results G roup Rate initial change final initial change final IA -50% 40 -10% 20 -50% IIA -25% 20 IIB -50% 20 IIIA -10% 20 IIIB -50% 20 IVA -50% 0 IVB -25% 40 20 -10% 25 -25% 15 -50% 28 -10% 12 -50% 10 -50% 30 -25% 12 -50% 28 -10% 20 -25% 13 -50% 31 -10% 9 -50% 12 -50% 28 -25% 9 31 -10% 27 -25% 14 -50% 33 -10% 7 -50% 13 -50% 27 -25% 33 27 14 34 6 13 27 initial change final -50% initial change final initial change final initial change final initial change final initial change final IB 7 0 -25% -50% -50% -10% -50% -25% -10% -50% 22 -25% 18 -50% 14 -50% 26 -10% 19 -50% 21 -25% 25 -10% 15 -50% 25 -25% 15 -50% 10 -50% 30 -10% 14 -50% 26 -25% 30 -10% 10 -50% 27 -25% 13 -50% 8 -50% 32 -10% 14 -50% 26 -25% 32 -10% -50% 27 13 33 14 26 33 7 7 7 Dynamic Equilibrium “The Pennies” Class Results http://chemconnections.org/general/chem120/equil-graph.html Simulator: http://chemconnections.org/Java/equilibrium/ Dynamic Equilibrium “The Pennies” http://chemconnections.org/general/chem120/equil-graph.html Chemical Equilibrium Consider A B [Refer to the Equilibrium Worksheet.] If the reaction begins with just A, as the reaction progresses: • [A] decreases to a constant concentration, • [B] increases from zero to a constant concentration. • When [A] and [B] are constant, equilibrium is reached. Chemical Equilibrium Graphical Treatment of Rates & Changes • Rate of loss of A = -kf [A]; decreases to a constant, • Rate of formation of B = kr [B]; increases from zero to a constant. • When -kf [A] = kr [B] equilibrium is reached. QUESTION The changes in concentrations with time for the reaction H2O(g) + CO(g) H2(g) + CO2(g) are graphed below when equimolar quantities of H2O(g) and CO(g) are mixed. Which of the comments given here accurately apply to the concentration versus time graph for the H2O + CO reaction? A. B. C. D. The point where the two curves cross shows the concentrations of reactants and products at equilibrium. The slopes of tangent lines to each curve at a specific time prior to reaching equilibrium are equal, but opposite, because the stoichiometry between the products and reactants is all 1:1. Equilibrium is reached when the H2O and CO curves (green) gets to the same level as the CO2 and H2 curves (red) begin. The slopes of tangent lines to both curves at a particular time indicate that the reaction is fast and reaches equilibrium. Answer B) is the only statement that accurately comments on this graph. When the stoichiometry is not 1:1 the slopes of tangent lines to both curves at a particular time reflect the stoichiometry ratio of the reactants. Chemical Equilibrium N2(g) + 3H2(g) 2NH3(g) Add nitrogen and hydrogen gases together in any proportions. Nothing noticeable occurs. Add heat, pressure and a catalyst, you smell ammonia => a mixture with constant concentrations of N2 , H2 and NH3 is produced. Start with just ammonia and catalyst. N2 and H2 will be produced until a state of equilibrium is reached. As before, a mixture with constant concentrations of nitrogen, hydrogen and ammonia is produced. Chemical Equilibrium N2(g) + 3H2(g) 2NH3(g) No matter what the starting composition of reactants and products, the same ratio of concentrations is realized when equilibrium is reached at a certain temperature and pressure. Chemical Equilibrium N2(g) + 3H2(g) The Previous Examples Graphically: 2NH3(g) QUESTION This is a concentration profile for the reaction N2(g) + 3H2(g) 2NH3(g) when only N2(g) and H2(g) are mixed initially. The figure shown here represents the concentration versus time relationship for the synthesis of ammonia (NH3). Which of the following correctly interprets an observation of the system? A. B C. D. At equilibrium, the concentration of NH3 remains constant even though some is also forming N2 and H2, because some N2 and H2 continues to form NH3. The NH3 curve (red) crosses the N2 curve (blue) before reaching equilibrium because it is formed at a slower rate than N2 rate of use. All slopes of tangent lines become equal at equilibrium because the reaction began with no product (NH3). If the initial N2 and H2 concentrations were doubled from what is shown here, the final positions of those curves would be twice as high, but the NH3 curve would be the same. Answer A) properly states the relationship between reactants and products in a system that has reached a dynamic equilibrium. At equilibrium, the rate of the forward reaction continues at a pace that is equal to the continued pace of the reverse reaction. Law of Mass Action (Equilibrium Expression) For a reaction: • jA + kB lC + mD The law of mass action is represented by the Equilibrium Expression: where K is the Equilibrium Constant. (Units for K will vary.) l m C D K A j Bk QUESTION One of the environmentally important reactions involved in acid rain production has the following equilibrium expression. From the expression, what would be the balanced chemical reaction? Note: all components are in the gas phase. K = [SO3]/([SO2][O2]1/2) A. B. C. D. SO3(g) SO2(g) + 2O2(g) SO3(g) SO2(g) + 1/2O2(g) SO2(g) + 2O2(g) SO3(g) SO2(g) + 1/2O2(g) SO3(g) Answer D) properly shows the product SO3 on the right and incorporates the previous exponents from the equilibrium expression as coefficients in the chemical equation. Equilibrium Expression 4 NH3(g) + 7 O2(g) 4 NO2(g) + 6 H2O(g) Write the Equilibrium Expression for the reaction. The expression will have either concentration units of mol/L (M), or units of pressure (atm) for the reactants and products. What would be the overall unit for K using Molarity and atm units respectively. 4 6 NO2 H 2O K 4 7 NH3 O2 K’s units = M -1= L/mol or atm-1 QUESTION Starting with the initial concentrations of: [NH3] = 2.00 M; [N2] = 2.00 M; [H2] = 2.00 M, what would you calculate as the equilibrium ratio once the equilibrium position is reached for the ammonia synthesis reaction? N2 + 3H2 2NH3 A. B. C. D. 1.00 0.250 4.00 This cannot be done from the information provided. Answer D) is the correct response. The concentrations given are for the INITIAL position. In order to calculate the K ratio of products to reactants the equilibrium position concentrations must be observed. Equilibrium Expressions 1) If a reaction is re-written where the reactants become products and products-reactants, the new Equilibrium Expression is the reciprocal of the old. Knew = 1 / Koriginal 2) When the entire equation for a reaction is multiplied by n, Knew = (Koriginal)n The Equilibrium Constant N2O4(g) 2NO2(g) NO2 Kc 0.212 N2O4 2 N2O4 1 Kc 4.72 2 NO2 0.212 The Equilibrium Constant N2O4(g) 2NO2(g) 2NO2(g) N2O4(g) The Equilibrium Constant N2O4(g) 2NO2(g) NO2 Kc 0.212 N2O4 2 2NO2(g) N2O4(g) N2O4 1 Kc 4.72 2 NO2 0.212 QUESTION One of the primary components in the aroma of rotten eggs is H2S. At a certain temperature, it will decompose via the following reaction. 2H2S(g) 2H2(g) + S2(g) If an equilibrium mixture of the gases contained the following pressures of the components, what would be the value of Kp? PH2S = 1.19 atm; PH2 = 0.25 atm; PS2 = 0.25 atm A. B. C. D. 0.011 91 0.052 0.013 ANSWER A) provides the correct Kp value. Whether the equilibrium constant is based on pressure or molarity, the ratio is always set to show products divided by reactants. In addition, the pressure must be raised to the power that corresponds to the coefficients in the balanced equation. Heterogeneous Equilibrium Heterogeneous Equilibria When all reactants and products are in one phase, the equilibrium is homogeneous. If one or more reactants or products are in a different phase, the equilibrium is heterogeneous. • CaCO3(s) CaO(s) + CO2(g) K = [CO2] Heterogeneous Equilibria CaCO3(s) CaO(s) + CO2(g) K = [CO2] •Experimentally, the amount of CO2 does not meaningfully depend on the amounts of CaO and CaCO3. •The position of a heterogeneous equilibrium does not depend on the amounts of pure solids or liquids present. QUESTION The liquid metal mercury can be obtained from its ore cinnabar via the following reaction: HgS(s) + O2(g) Hg(l) + SO2(g) Which of the following shows the proper expression for Kc? A. B. C. D. Kc = [Hg][SO2]/[HgS][O2] Kc = [SO2]/[O2] Kc = [Hg][SO2]/[O2] Kc = [O2]/[SO2] Answer B) correctly presents the product to reactant ratio. Recall that pure liquids and solids are not shown in the equilibrium constant expression. QUESTION At a certain temperature, FeO can react with CO to form Fe and CO2. If the Kp value at that temperature was 0.242, what would you calculate as the pressure of CO2 at equilibrium if a sample of FeO was initially in a container with CO at a pressure of 0.95 atm? FeO(s) + CO(g) Fe(s) + CO2(g) A. B. C. D. 0.24 atm 0.48 atm 0.19 atm 0.95 atm ANSWER C) provides the correct pressure in this equilibrium system. Solids do not appear in the equilibrium expression, so Kp = PCO2/PCO. Also the reaction indicates a 1:1 ratio between the change in CO and CO2. Therefore Kp = X/(0.95 – X) The Equilibrium Constant K Calculating Equilibrium Constants • Tabulate 1) initial and 2) equilibrium concentrations (or partial pressures). • Having both an initial and an equilibrium concentration for any species, calculate its change in concentration. • Apply stoichiometry to the change in concentration to calculate the changes in concentration of all species. • Deduce the equilibrium concentrations of all species. CH3COOC2H5(aq) + H2O(aq) CH3COOH(aq) + C2H5OH (aq) Kc: 5.00 ml of ethyl alcohol, 5.00 ml of acetic acid and 5.00 ml of 3M hydrochloric acid were mixed in a vial and allowed to come to equilibrium. The equilibrium mixture was titrated and found to contain 0.04980 mol of acetic acid at equilibrium. What is the value of Kc ? 1) Calculate the initial molar concentrations (moles are OK in this case). 2) Use the equilibrium concentration of acetic acid to determine the changes and the equilibrium concentrations of the others. 3) Place the equilibrium values into the equilibrium expression to find it’s value. CH3COOC2H5(aq) + H2O(aq) Initial (mol) 0 Change +0.0375 Equilibrium 0.0375 Kc = 0.214 CH3COOH(aq) + C2H5OH (aq) 0.261 0.0873 0.0856 +0.0375 -0.0375 -0.0375 0.2985 0.0498 0.0481 0.0873 - 0.0498 = 0.0375 Calculating Equilibrium Constants •1) Write the Equilibrium Expression for the hydrolysis of ethyl acetate and calculate Kc from the following equilibrium concentrations. •2) Write the Equilibrium Expression for the formation of ethyl acetate from acetic acid and calculate Kc from the following equilibrium concentrations. Ethyl acetate = 0.01217 M; Ethanol = 0.01623 M Acetic acid = 0.01750 M ; Water = 0.09267 M Calculating Kc from Concentration Data 2 HI(g) H2 (g) + I2 (g) 4.00 mol HI was placed in a 5.00 L vessel at 458°C, the equilibrium mixture was found to contain 0.442 mol I2. What is the value of Kc ? Calculate the molar concentrations, and put them into the equilibrium expression to find it’s value. Starting conc. of HI = 4.00 mol = 0.800 M 5.00 L 0.442 mol Equilibrium conc. of I2 = = 0.0884 M 5.00 L Conc. (M) Starting Change Equilibrium 2HI(g) 0.800 - 2x 0.800 - 2x H2 (g) 0 x x I2 (g) 0 x x = 0.0884 Calculating Kc from Concentration Data (continued) 2 HI(g) H2 (g) + I2 (g) [HI] = M = (0.800 - 2 x 0.0884) M = 0.623 M [H2] = x = 0.0884 M = [I2] Kc = [H2] [I2] [HI]2 = ( 0.0884)(0.0884) (0.623)2 = 0.0201 What does the value 0.0201 mean? Does the decomposition proceed very far under these temperature conditions? Note: The initial concentrations, and one at equilibrium were provided. The others that were needed to calculate the equilibrium constant were deduced algebraically. Calculation of Equilibrium Concentrations The same steps used to calculate equilibrium constants are used. Generally, we do not have a number for the change in concentrations line. Therefore, we need to assume that x mol/L of a species is produced (or used). The equilibrium concentrations are given as algebraic expressions.Solution of a quadratic equation may be necessary. If you are interested in this interactive Flash tool, send Dr. R. an e-mail and he will send it you as an attachment. http://chemconnections.org/general/chem120/UsinganEquilibriumTableII.swf QUESTION The weak acid HC2H3O2, acetic acid, is a key component in vinegar. As an acid the aqueous dissociation equilibrium could be represented as HC2H3O2(aq) H+(aq) + C2H3O2 –(aq). At room temperature the Kc value, at approximately 1.8 10–5, is not large. What would be the equilibrium concentration of H+ starting from 1.0 M acetic acid solution? A. B. C. D. 1.8 10–5 M 4.2 10–3 M 9.0 10–5 M More information is needed to complete this calculation. ANSWER B) is correct assuming that 1.0 – X can be approximated to 1.0. The relatively small value for K indicates that, compared to 1.0, X would not be large enough to include in the calculation. The equilibrium expression could be simplified to K = X2/1.0. A quick test of this hypothesis could be made by using the 4.2 10–3 value as X and checking the right side of the expression to see if it was the same as 1.8 10–5. Equilibrium Concentration Calculations from Initial Concentrations and Kc The reaction to form HF from hydrogen and fluorine has an equilibrium constant of 115 at temperature T. If 3.000 mol of each component is added to a 1.500 L flask, calculate the equilibrium concentrations of each species. H2 (g) + F2 (g) Solution: 2 [HF] Kc = = 115 [H2] [F2] 2 HF(g) [H2] =3.000 mol = 2.000 M 1.500 L [F2] = 3.000 mol = 2.000 M 1.500 L 3.000 mol [HF] = = 2.000 M 1.500 L Equilibrium Concentration Calculations H2 (g) + F2 (g) 2 HF(g ) (Continued) Concentration (M) H2 F2 HF __________________________________________ Initial 2.000 2.000 2.000 Change -x -x +2x Final 2.000-x 2.000-x 2.000+2x 2 2 2 [HF] (2.000 + 2x) (2.000 + 2x) Kc = = 115 = = [H2][F2] (2.000 - x) (2.000 - x) (2.000 - x)2 Taking the square root of each side: + 2x) =10.7238 (115)1/2 =(2.000 (2.000 - x) [H2] = 2.000 - 1.528 = 0.472 M [F2] = 2.000 - 1.528 = 0.472 M [HF] = 2.000 + 2(1.528) = 5.056 M x = 1.528 2 2 [HF] (5.056 M) Kc = = [H2][F2] (0.472 M)(0.472 M) check: Kc = 115 Using the Quadratic Equation to solve for an unknown The gas phase reaction of 2 moles of CO and 1 mole of H2O in a 1L vessel: Concentration (M) Initial Change Equilibrium [CO2][H2] CO(g) 2.00 -x 2.00-x + H2O(g) CO2(g) 1.00 -x 1.00-x 0 +x x + H2(g) 0 +x x 2 (x) (x) x Kc = = = = 1.56 2 [CO][H2O] (2.00-x)(1.00-x) x - 3.00x + 2.00 We rearrange the equation: 0.56 x2 - 4.68 x + 3.12 = 0 ax2 + bx + c = 0 quadratic equation: 2 - 4ac b + b x= [CO] = 1.27 M 2a [H2O] = 0.27 M 2 [CO2] = 0.73 M x = 4.68 + (-4.68) - 4(0.56)(3.12) = 7.6 M 2(0.56) [H2] = 0.73 M and 0.73 M Reaction Quotient (Q) vs. K K vs. Q: Equilibrium Constants Has equilibrium been reached? Has equilibrium been reached? Q is the “reaction quotient” for any general reaction, for example: aA + bB mM + pP M P Q a b A B m p [A], [B], [P], and [M] are Molarities at any time. Q = K only at equilibrium Q vs. K: Predicting the Direction of Reaction If Q < K then the forward reaction must occur to reach equilibrium. (i.e., reactants are consumed, products are formed, the numerator in the equilibrium constant expression increases and Q increases until it equals K). If Q > K then the reverse reaction must occur to reach equilibrium (i.e., products are consumed, reactants are formed, the numerator in the equilibrium constant expression decreases and Q decreases until it equals K). Calculating Reaction Direction and Equilibrium Concentrations Two components of natural gas can react according to the following chemical equation: CH4(g) + 2 H2S(g) CS2(g) + H2(g) 1.00 mol CH4, 1.00 mol CS2, 2.00 mol H2S, and 2.00 mol H2 are mixed in a 250 mL vessel at 960°C. At this temperature, Kc = 0.036. (a) In which direction will the reaction go? (b) If [CH4] = 5.56 M at equilibrium, what are the concentrations of the other substances? Calculate Qc and compare it with Kc. Based upon (a), we determine the sign of each component for the reaction table and then use the given [CH4] at equilibrium to determine the others. Solution: [CH4] = 1.00 mol = 4.00 M 0.250 L [H2S] = 8.00 M, [CS2] = 4.00 M and [H2 ] = 8.00 M Calculating Reaction Direction and Equilibrium Concentrations [CS2] [H2]4 Qc = = 2 [CH4] [H2S] 4.00 x (8.00)4 = 64.0 4.00 x (8.00)2 Compare Qc and Kc: Qc > Kc (64.0 > 0.036, so the reaction goes to the left. Therefore, reactants increase and products decrease their concentrations. (b) Set up the reaction table, with x = [CS2] that reacts, which equals the [CH4] that forms. Concentration (M) CH4 (g) + 2 H2S(g) CS2(g) + 4 H2(g) Initial Change Equilibrium 4.00 +x 4.00 + x 8.00 +2x 8.00 + 2x 4.00 -x 4.00 - x 8.00 -4x 8.00 - 4x Solving for x at equilibrium: [CH4] = 5.56 M = 4.00 M + x x = 1.56 M Calculating Reaction Direction and Equilibrium Concentrations x = 1.56 M = [CH4] Therefore: [H2S] = 8.00 M + 2x = 8.00 M + 2(1.56 M) = 11.12 M [CS2] = 4.00 M - x = 4.00 M - 1.56 M = 2.44 M [H2] = 8.00 M - 4x = 8.00 M - 4(1.56 M) = 1.76 M [CH4] = 1.56 M Le Châtelier’s Principle . . . if a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change. Le Châtelier’s Principle NO2 - N2O4 Temperature Dependence of K Changes on the System 1. Concentration: The system will shift concentrations away from the added component. K remains the same. 2. Temperature: K changes depending upon the reaction. If endothermic, heat is treated as a “reactant”, if exothermic, heat is a “product”. Endo- > K increases; Exo- > K decreases. if H > 0, adding heat favors the forward reaction, if H < 0, adding heat favors the reverse reaction. Chemical Equilibrium Which is favored by raising the temperature in the following equilibrium reaction? A+B or C QUESTION The following table shows the relation between the value of K and temperature of the system: At 25°C; K = 45; at 50°C; K = 145; at 110°C; K = 467 (a) Would this data indicate that the reaction was endothermic or exothermic? (b) Would heating the system at equilibrium cause more or less product to form? A. B. C. D. Exothermic; less product Exothermic; more product Endothermic; less product Endothermic; more product ANSWER D) makes correct assumptions using Le Châtelier’s principle. The increase in K with temperature indicates that the reaction uses energy to produce a higher ratio of product to reactant at equilibrium. The stress of heat for an endothermic reaction causes more product to form. Changes on the System (continued) 3. Pressure: a. Addition of inert gas does not affect the equilibrium position. b. Decreasing the volume shifts the equilibrium toward the side with fewer moles. Kp = Kc (RT)n n = ngas (products) - ngas (reactants) • As the volume is decreased pressure increases. • Le Châtelier’s Principle: if pressure is increased the system shifts to minimize the increase. QUESTION The balanced equation shown here has a Kp value of 0.011. What would be the value for Kc ?(at approximately 1,100°C) 2H2S(g) 2H2(g) + S2(g) A. B. C. D. 0.000098 0.011 0.99 1.2 Answer A) is obtained from Kp = Kc(RT)n when T is expressed in K and the expression is solved for Kc Changes on the System (continued) 4. The Effect of Catalysts A catalyst lowers the activation energy barrier for any reaction….in both forward and reverse directions! A catalyst will decrease the time it takes to reach equilibrium. A catalyst does not effect the composition of the equilibrium mixture. Energy vs. Reaction Pathway Putting it all Together N2(g) + 3H2(g) 2NH3(g) Putting it all Together N2(g) + 3H2(g) 2NH3(g) Putting it all Together N2(g) + 3H2(g) 2NH3(g) Putting it all Together N2(g) + 3H2(g) 2NH3(g)